assuming you meant
$\displaystyle \frac {-2}{\sqrt{4x^2} (\sqrt{2x} + \sqrt{2x})}$ (which is not actually what you typed)
you are correct.
note that (since x is positive), $\displaystyle \sqrt{4x^2} = 2x$, also, $\displaystyle \sqrt{2x} + \sqrt{2x} = 2 \sqrt{2x}$, and so you have
$\displaystyle \frac {-2}{2x \cdot 2\sqrt{2x}}$
now the 2's cancel and we have
$\displaystyle \frac {-1}{2x \cdot \sqrt{2x}}$
but $\displaystyle \sqrt{2x} = (2x)^{\frac 12}$, and so, $\displaystyle 2x \cdot \sqrt{2x} = 2x \cdot (2x)^{\frac 12} = (2x)^{\frac 32}$, which gives
$\displaystyle \frac {-1}{(2x)^{3/2}}$
or if you prefer
$\displaystyle \frac {-1}{(\sqrt{2x})^3}$
a quick check by differentiating $\displaystyle \frac 1{\sqrt{2x}} = (2x)^{-1/2}$ using the chain rule confirms that this is the right answer.
the simplifying may seem daunting, but it depends on how you do it. for example, it probably would have been best if we had not "simplified" the denominator in one of the steps to get $\displaystyle \sqrt{4x(x + h)}$. otherwise, with practice, such simplifications should be easy to do quickly